High critical current density and high-tolerance superconductivity in high-entropy alloy thin films

High-entropy alloy (HEA) superconductors—a new class of functional materials—can be utilized stably under extreme conditions, such as in space environments, owing to their high mechanical hardness and excellent irradiation tolerance. However, the feasibility of practical applications of HEA superconductors has not yet been demonstrated because the critical current density (Jc) for HEA superconductors has not yet been adequately characterized. Here, we report the fabrication of high-quality superconducting (SC) thin films of Ta–Nb–Hf–Zr–Ti HEAs via a pulsed laser deposition. The thin films exhibit a large Jc of >1 MA cm−2 at 4.2 K and are therefore favorable for SC devices as well as large-scale applications. In addition, they show extremely robust superconductivity to irradiation-induced disorder controlled by the dose of Kr-ion irradiation. The superconductivity of the HEA films is more than 1000 times more resistant to displacement damage than that of other promising superconductors with technological applications, such as MgB2, Nb3Sn, Fe-based superconductors, and high-Tc cuprate superconductors. These results demonstrate that HEA superconductors have considerable potential for use under extreme conditions, such as in aerospace applications, nuclear fusion reactors, and high-field SC magnets.


Supplementary Figures 1 to 8
Supplementary

Supplementary References
Supplementary Table 1. Atomic ratio of Ta-Nb-Hf-Zr-Ti HEA superconducting (SC) thin films. Results obtained from energy dispersive spectroscopy (EDS) for the atomic ratios of Ta-Nb-Hf-Zr-Ti HEA target and SC thin films fabricated via the pulsed laser deposition (PLD) technique at various substrate temperatures (Ts): 270,370,470,500,520,540,570, and 620 ºC. No significant differences were observed among the compositional ratios of the films. The deviation of the chemical composition ratio between the target and the HEA thin film is related to the relatively larger sputtering yield of Ti and Zr atoms than other constituent elements [S1,S2]. The similar atomic ratios of each HEA film, regardless of Ts, indicates that the sticking coefficient of each element is not significantly different.

Supplementary Figures 1 to 8
Supplementary Figure 1. EDS results for Ta-Nb-Hf-Zr-Ti HEA target. EDS spectra of HEA target used for the deposition of HEA SC thin films in this study. Except the constituent atoms of Ta-Nb-Hf-Zr-Ti HEA superconductors, the additional peaks in the EDS analysis are related to Fe impurity generated during the mechanical processing of ball milling. In general, high-energy ball milling processes often produce additional impurities from the milling tools [S3]. Stainless steel was used for the milling tool in this study, but Cr and Ni impurities were not detected within the EDS resolution.

Supplementary Figure 2. EDS results for Ta-Nb-Hf-Zr-Ti HEA SC thin films. a-h, EDS
spectra of Ta-Nb-Hf-Zr-Ti HEA SC thin films fabricated at Ts = 270-620 ºC for a large area and a droplet region. The difference in atomic ratios between the large area and the droplet region is negligible. Here, the peaks of elements C, O, and Al due to general contamination and Al2O3 substrate were not indicated. Ta [S7,S8]. (d) HEA SC thin films deposited at Ts = 500, 520, and 540 o C. All the films show considerably larger Jc values than the bulk samples. In addition, the film with the highest Tc, deposited at 520 o C, shows the highest Jc at low fields, whereas the Jc of the film fabricated at 500 o C has better field performance at high fields. A large flux jump was observed at 2.0 K for the HEA SC thin films with a relatively higher Tc, which resulted in a smaller low-field Jc compared with that at 4.2 K. The flux jump is attributed to thermomagnetic instability [S7,S8]; thus, the Jc value of an HEA SC thin film can be increased by reducing the thermal instability. The magnetic field dependence of Jc can be estimated from the M-H loops by using Bean's critical state model (Jc = 30ΔM/d).

Supplementary
Here, ΔM is the difference of M value at the same magnetic field in the irreversible regions, as indicated in Supplementary Fig. 7a, and d is the corresponding diameter of the total area, A = π(d/2) 2 , of the film's surface, as described in the inset of Supplementary Fig. 7b. The Jc(H) for all HEA SC thin films presented in this study was determined from the above relation. On the other hand, the Jc for the bulk sample with a rectangular shape is generally estimated from the relation Jc = 20ΔM/[w(1-w/3a)], where w and a is width and length, respectively, for w < a [S12,S13].